I have seen players calling not only 1 but 4 support vessels during combat. At first I thought this was a special Tactical player ability. Now I don't know anymore. Is this the regular Tactical fleet with duty officer assist or how do I pull off the trick?

Science Captain's get a power called Photonic Fleet which lets them call in 3 random ships of their faction.

If you are below 50% health you can use the ability "Fleet Support" to summon a random allied ship.

If you have the Distress beacons from the Romulan Reptutation system you can summon various Romulan ships. A Mogai, flight of Birds of Prey, or a D'deridex, I believe, depending on which beacon you use.

I know of no other sources to gain additional allied ships.

If you feel Keel'el's effect is well designed, please, for your own safety, be very careful around shallow pools of water.